Resizing Brass for Wildcats?

I have a 6mm/06 that my grandfather built in the 60's. He was a gunsmith and also had a set of dies made for it by RCBS. Hasn't been fired in maybe 35-40 years because I don't have any brass for it. (had a couple boxes at one time... but you know how these things go) I shot it a bunch back in the day, though. It's a tack-driving screamer! I don't have any ballistic info but I remember Grandpa saying he thought the MV was well over 3,500 FPS, with a 96 grain bullet.

I want to get it back in bench-shooting condition (doesn't even have a scope, currently) I have been considering re-chambering it for something more readily available but, since I just discovered that I actually have about 3,000 6mm bullets on hand, I've decided to start loading for it, at least until I run out of 6mm supplies... Or until I shoot the barrel out. It's gonna get hot!

It should certainly be easy to neck .25\06 brass down to .244 (that's what my grandad did) but, since I also own a .25\06, I would prefer to use something else just so that I can tell them apart from the .25's by sight.

I have a bunch of .30/06 brass, which would certainly be distinguishable from .244 at a glance. But one thing I'm worried about here is having necks end up too thick. I may have to turn down the outsides of the case necks after trimming to length, which means a lot more work. That brass has to go somewhere, and I assume it won't all go into growing the neck length. I have a trimmer but, no way to shave off the OD. If case necks thicken and I don't turn the necks, when I run the newly formed cases into the sizer die, the inside diameter might be too small to allow the bullet to fit without wanting to buckle the neck/shoulder junction. If I am able to seat the bullet into the case without turning them, the bullet will force the too thick brass in the neck back out to the sides, and the case may be too tight to fit the chamber, or worse, still fit the chamber but be thick enough that the case neck can't expand enough to properly release the bullet when fired, resulting in skyrocketing pressure. Maybe even into the disaster zone... Looking at the case dimensions, it looks like I might be able to use .270 Win brass, which would mitigate this risk somewhat.

One question I have is, can .30 or .270 cal, in its annealed state, be necked down to .244 with one pass, or will I need an intermediate die? Do I want to anneal before or after resizing? Or both? My grandfather obviously knew all this stuff. We were close and I absorbed a lot of information from him. But seem there are always questions you forgot to ask someone who isn't around anymore... Wish I knew a Medium. I could hold a seance.

Any further tips on resizing brass would be welcome.